How do you find two consecutive odd integers whose sum is 196?

2 Answers
Apr 25, 2016

Answer:

#97 and 99#

Explanation:

There is at least two ways of doing this: This is my approach

#color(blue)("Step 1")# Define a number so that it is always even

#" "#Let #n# be any number then #2n# is always even.

#color(blue)("Step 2")# Modify the defined number so that the result is always odd

#" "#If #2n# is always even then #2n+1# is always odd
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the first odd number be #2n+1#
Then the second odd number is #(2n+1)+2=2n+3#

Thus our given condition is such that:

#(2n+1)+(2n+3)=196#

#=>4n+4=196#

Subtract 4 from both sides

#=>4n=192#

Divide both sides by 4

#=>n=192/4=48#

But the first number is #2n+1 = 2(48)+1 = 97#

So the second number is #97+2=99#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check: #97+99= 196#

Apr 25, 2016

Answer:

Another way

Explanation:

Let the first number be #n#
Let the second number be #n+2#

Then #n+n+2=196#

#2n+2=196#

Subtract 2 from both sides

#2n=194#

Divide both sides by 2

#n=194/2= 97#

The first number is 97 so the second is 97+2=99

#color(red)("Notice that the " 2n + 2" is of the same format as that in my")##color(red)("other solution of "4n+4)#